Question

In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP: PB = 1: 2. Write down the coordinates of A and B.

Answer 1

Let (x, 0) and (0, y) be the coordinates of A and B respectively.
Point P divides AB in the ratio of 1: 2
So coordinates of P
4 = `(1 xx 0 + 2 xx x )/(1 + 2)`

⇒ 2x = 4 x 3
⇒ x = 6
Also -2 = `(2 xx 0 + 1 xx y)/(1 + 2)`
⇒ -6 = y
⇒ y = -6.
Hence, the coordinates of A and B are (-6, 0) and (0, 6) respectively.